A Study of Disjoint Set Union in Programming Competitions

DOI: https://doi.org/10.62517/jbdc.202301401

Author(s)

Zijie Shen, Ruixiang Li, Junping Shi*

Affiliation(s)

The School of Computer Science and Engineering, Jishou University, Jishou, Hunan, China *Corresponding Author.

Abstract

Disjoint Set Union (DSU) is a tree data structure, which is used to effectively deal with the problems of merging and querying disjoint sets. The DSU algorithm can be used to merge sets and query to which set the node belongs. The DSU algorithm is usually implemented using arrays and tree structures, but there are also methods that use hash tables. The DSU algorithm has a wide range of applications in the connectivity of graph theory, social network and image processing. It helps researchers better understand and analyze set operations, provides a basis for subsequent work, and promotes the solution and optimization of various problems in the field. At the same time, in the programming competition of college students, the use of DSU is more frequent, usually the use of set query is more, resulting in high time complexity and unable to solve the problem quickly. Therefore, path compression strategy is introduced to significantly improve the efficiency of set query. Finally, the application of path compression in union search is introduced in the form of programming competition.

Keywords

Disjoint Set Union; Tree Data Structure; Merging; Querying; Path Compression Strategy

References

[1]Yonghui Wu and Jiande Wang. Algorithm Design Practice for Collegiate Programming Contests and Education. Routledge, 2018, 706-706. [2]Clifford A. Shaffer. A Practical Introduction to Data Structures and Algorithm Analysis. Prentice Hall PTR, 2000, 512-512. [3]G. J. Chaitin. Algorithmic information theory. IBM Journal of Research and Development, 1977, 21(4):350-359. [4]Galler, Bernard A. and Fisher, Michael J. An improved equivalence algorithm. Association for Computing Machinery, 1964, 7(5):301-303. [5]Eleni Stroulia and Stan Matwin. Advances in Artificial Intelligence. Proceedings of the 14th Biennial Conference of the Canadian Society on Computational Studies of Intelligence, Berlin, Heidelberg, 2001. [6]Chen, Qingyun, Laekhanukit, Bundit, Liao Chao et al. Survivable Network Design Revisited: Group-Connectivity. 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), 2022, 278-289. [7]Chen X, Wang Y, Dong H, et al. Network Representation Learning Based On Random Walk Of Connection Number. International journal of innovative computing, information and control, 2022, 18(3):883-900. [8]Hwang J H, Shin H U. Effects of Job Search Behavior Patterns on the Employment of Persons with Disabilities in Korea through Social Network Analysis. Journal of rehabilitation, 2023, 89(2):50-57. [9]Patterson, C. L. and Buechler, Guenther. Digital image processing at the Aerospace Corporation. Computer, 1974, 7(5):46-52. [10]Gundala, Laxmi Amulya and Spezzano, Francesca. A Framework for Predicting Links between Indirectly Interacting Nodes. 2018 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM), 2018, 544-551. [11]Golumbic, Martin Charles and Shamir, Ron. Complexity and algorithms for reasoning about time: a graph-theoretic approach. Association for Computing Machinery, 2010, 40(5):1108-1133.